Data Sufficiency MCQ Set 1

Correct Answer: A

Explanation:

Algebra Applied problems; Simultaneous equations; Inequalities

Let x represent the number of $100 certificates sold, and let y represent the number of $10 certificates sold. Then the given information can be expressed as x+y = 20 or thus y = 20- x. The value of the $100 certificates sold is 100x, and the value of the $10 certificates sold is 10y.

• (1) From this, it is known that 100* +10y > 1,650. Since y = 20- x, this value can be substituted for y, and the inequality can be solved for x:
  100* + 10y > 1,650
  100* +10(20 -x) >1,650 substitute for y
  100* + 200 -10* > 1,650 distribute
  90* +200 > 1,650 simplify
  90* > 1,450 subtract 200 from both sides
  *>16.1

  Thus, more than 16 of the $100 certificates were sold. If 17 $100 certificates were sold, then it must be that 3 $10 certificates were also sold for a total of $1,730, which satisfies the condition of being between $1,650 and $1,800. If, however, 18 $100 certificates were sold, then it must be that 2 $10 certificates were sold, and this totals $1,820, which is more than $1,800 and fails to satisfy the condition. Therefore, 3 of the $10 certificates were sold; SUFFICIENT.

• (2) From this it can be known only that the number of $10 certificates sold was 4 or fewer; NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.

Correct Answer: E

Explanation:

Arithmetic operations: If the units digit of nis greater than 2, then it can only be the digits 3, 4, 5, 6, 7, 8, or 9.

• (1) To solve this problem, it is necessary to find a digit that is the same as the units digit of its square. For example, both 43 squared (1,849) and 303 squared (91,809) have a units digit of 9, which is different from the units digit of 43 and 303. However, 25 squared (625) and 385 squared (148,225) both have a units digit of 5, and 16 and 226 both have a units digit of 6 and their squares (256 and 51,076, respectively) do, too. However,there is no further information to choose between 5 or 6; NOT sufficient.
• (2) Once again, 5 and 6 are the only numbers which, when cubed, will both have a 5 or 6 respectively in their units digits. However, the information given does not distinguish between them; NOT sufficient.

Since (1) and (2) together yield the same information but with no direction as to which to choose, there is not enough information to determine the answer.

The correct answer is E; both statements together are still not sufficient.

Correct Answer: E

Explanation:

Arithmetic Properties of numbers

• (1) These are factors of p, but it is not clear that they are the only factors of p; NOT sufficient.
• (2) These are factors of p, but it is not clear that they are the only factors of p;NOT sufficient.

Taken together, (1) and (2) overlap, but again there is no clear indication that these are the only factors of p.

The correct answer is E; both statements together are still not sufficient.

Correct Answer: E

Explanation:

Arithmetic operations

• (1) This does not give any information as to the call's cost per minute; NOT sufficient.
• (2) From this, it can be determined only that the call was longer than one minute and that the charge for the first minute was $0.50 more than the charge for each succeeding minute;NOT sufficient.

Taking (1) and (2) together, the number of minutes cannot be determined as long as the cost of each minute after the first is unknown.For example, if the cost of each minute after the first minute were $0.40, then the cost of the first minute would be $0.90. Then the total cost of the other minutes would be $6.50 - $0.90 = $5.60, and $5.60+ $0.40 would yield 14. In this case, the time of the call would be 1 +14 = 15 minutes. If, however, the cost of each minute after the first minute were $0.15, then the cost of the first minute would be $0.65. Then $6.50 - $0.65 would be $5.85, and this in turn, when divided by $0.15,would yield 39 minutes, for a total call length of 40 minutes. More information on the cost of each minute after the first minute is still needed.

The correct answer is E; both statements together are still not sufficient.

Correct Answer: E

Explanation:

Geometry Triangles

The perimeter of a triangle is the sum of all three sides. In the case of an isosceles triangle, two of the sides are equal.To determine the perimeter of this triangle, it is necessary to know both the length of an equal side and the length of the base of the triangle.

• (1) Only gives the length of one side; NOT sufficient.
• (2) Only gives the length of one side; NOT sufficient.

Since it is unclear whether MN or NP is one of the equal sides, it is not possible to determine the length of the third side or the perimeter of the triangle. The perimeter could be either ((2)(16)) +20 =52 or ((2)(20)) +16=56.

The correct answer is E; both statements together are still not sufficient.

Correct Answer: E

Explanation:

Arithmetic Percents

• (1) With only this, it cannot be known what percent of the retailers not owning their own store had purchased computers, and so it cannot be known how many retailers purchased computers overall; NOT sufficient.
• (2) While this permits the percent of owners and non owners in the survey to be deduced, the overall percent of retailers who had purchased computers cannot be determined;NOT sufficient.

Using the information from both (1) and (2), the percent of surveyed owner-retailers who had purchased computers can be deduced, and the percent of non owner-retailers can also be deduced. However, the information that would permit a determination of either the percent of non owner-retailers who had purchased computers or the overall percent of all retailers (both owners and non owners) who had purchased computers is still not provided.

The correct answer is E; both statements together are still not sufficient.